Introduction

The average tuition cost for university has risen in the past 20 or so years, and we are interested in comparing the changes in tuition and minimum wage. By analyzing the cost of tuition, the minimum wage, and the cost of living index, we can see how prices have changed since 2000 and where expenses differ in U.S. regions.

Cost of Living Data

The first data set we used was from Numbeo. It contained the average cost of living index for each state in the United States in 2018. It has 132 cities with two corresponding values. The first value is the ‘cost of living index’ which is an indicator of consumer goods like groceries, restaurants, transportation, and utilities. The values are indices relative to New York City. For New York City, all indices are 100. The second value is ‘rent index,’ and it works the same as the ‘cost of living index.’ If another city has a rent index of 120, this means on average that cities rent is 20% more expensive than New York City.

An additional dataset contains the latitude and longitude values for every 28,889 cities. This was only used to enable a spatial visualization of our cost of living dataset.

Minimum Wage Data

The second dataset we used was from the U.S. Department of Labor. It contained the minimum wage for each state from the years 1969-2018. For minimum wage values lower than the federal, states are allowed to set lower rates for state specific reasons like number of employees and annual gross sales.

Tuition Data

The first dataset we used was from the Digest of Education Statistics. It contained the average tuition and fees along with board rates for each type of university in the United States by the year for 1963-2018.

Challenges

Since all our data was scraped from the internet, we encountered a lot of cleaning issues. These issues mostly consisted of numeric data holding character and NA values.

We tried to merge the three main datasets, but due to different sizes with different variables, we found that merging the datasets would become inaccurate. Datapoints would get dropped when forcing a merge, so instead we opted to use the datasets separately.

Data Cleaning

Initial exploration revealed that some data processing was needed before we could proceed with further visualization. Our data went back to 1969. We only want to look at the last 20 years so we deleted all the data from 1969-1999.

In the minimum wage date, some states had two minimum wages in one year. This could be because of different parts of the state having a higher minimum then the states, like Minnesota and Minneapolis, or they had a change in the middle of the year. To use this data, we took the average of the two minimum wages if a state had multiple wages for one year.

The data set for tuition cost was also divided into current and constant costs. Since we wanted to compare the costs throughout the years, we only used current, in order to read the cost in our current value of a dollar.

Cost of Living

To explore areas that have a relatively high cost of living, both the ‘Cost of Living Index’ and ‘Rent Index’ were examined. The ‘Cost of Living Index’ for each major city is mapped below with the size and color of the point an output of the ‘Cost of Living Index’. The larger and more yellow the point, the greater the value of ‘Cost of Living Index’ for that city.

‘Cost of Living Index’ has two significant areas of spiked prices. Expensive areas can be seen on the east and west coasts. The states of California and Florida have an especially high concentration of cities with a high ‘Cost of Living Index’; however, California and Florida do have the highest proportion of major cities from the dataset with 13 cities being from California and 10 from Florida out of 132 total cities.

The ‘Rent Index’ was mapped the same way as the ‘Cost of Living Index’ and the same geographical pattern was visible; however, the ‘Rent Index’ contained more extreme values than that of ‘Cost of Living.’

For further investigation, the distribution of both variables were plotted next to each other in a boxplot. Revealing that the rent can be very high in extrema cities in comparison to the median. For example, New York City is 65% more expensive for rent than that of the median. However, the difference of the cost of living in these extreme rent cities compared to the median will be much smaller. For example, New York City is 25% more expensive for cost of living than the median.

Minimum Wage

The minimum wage for each state was mapped. There is a concentration of higher minimum wages on the west and upper east coast. This fits the trend of ‘Cost of Living Index’ sans the lower east coast. Some of the Southern states (Alabama,Louisiana,etc.) do not have a state minimum wage and adopt the federal. This could cause the expense of the state to not be reflected in their minimum wage. Since minimum wage is integrated with government policy, minimum wage data may be inaccurate to judge overall wage.

A scatterplot was created to view the relationship between state and minimum wage. Some states have certain jobs that allow them to go below the minimum wage, such as Oklahoma and Georgia. These states have particularly low minimum wages because we averaged the range of wages given. In reality, the minimum wage would be closer to the federal wage of $7.25, but we had no information to get a more accurate indication of what the true value is.

Best/Worst State

The minimum wage and tuition data was subset into just the 2018 data in order to find the best and worst state based on cost of living and minimum wage. The cost of living dataset had multiple cities per certain states, so the median of the states’ cost of living index was found and visualized in a scatter plot.

The minimum wage dataset was subset into three groups: above $10/hr, between $10 and $8/hr, and below $8/hr. Four scatterplots were created, one for all states minimum wages, and a scatterplot for each subgroup that was created.

After creating these plots, the plots were compared to find the state with the highest cost of living and lowest minimum wage, and the lowest cost of living with the highest minimum wage. Similar states were compared by using their medians.

Showing the boxplots and medians of the best state (Arizona) and the worst state (Pennsylvania).

## [1] 64.935

## [1] 78.66

Tuition

An animated plot was used to show the rise in tuition prices per academic year for 1999-2018. We used out of state tuition and changed the name of Year to make it easier to work with.

The correlation between minimum wage and tuition was found after observing that both increase every year. A new dataset containing the mean wages for each year was used and correlated with the tuition data set. As seen below, mimimum wage and tuition have a high positive correlation. This means that as tuition increases so does mimimum wage at a similar rate.

## [1] 0.984901

Showing if a realtionship exists between the plots of In State tuition and Out of State tuition

After finding the trend in values for in state and out of state tuition based on the above plots, we wanted to see if a prediction model could be used to predict a new value for out of state tuition based on a given value for in state tuition. Using the model, we predicted the out of state tuition of an academic year based on a given input value for in state tuition. Since the linear model is very simple to understand and use, the easiest way to predict a value was to use the coefficient estimates from the model. From the linear model we can see how well the data was fitted to the model based on the r-squared of 0.9988.This helped us determine that on average in state and out of state tuition are linearly related.

## 
## Call:
## lm(formula = tuition2 ~ tuition3, data = tuition)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -225.23 -129.89  -17.37  133.31  321.72 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 446.21121  161.71076   2.759   0.0134 *  
## tuition3      1.66975    0.01337 124.912   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 167.4 on 17 degrees of freedom
## Multiple R-squared:  0.9989, Adjusted R-squared:  0.9988 
## F-statistic: 1.56e+04 on 1 and 17 DF,  p-value: < 2.2e-16
## [1] 42690.84

Conclusion

Living on the coast is more expensive than inland. There are more cities with extreme rent costs than that of cost of living costs. This could be due to space being a limited commodity while the overall cost of consumer goods are an abundant commodity. Individuals who live in higher cost of living areas can expect to have a higher minimum wage except for the Southern-east coast. Tuition and minimum wage have a strong positive correlation. This means that as tuition increases, minimum wage also increases at a similar rate. Using minimum wage and the cost of living index, Arizona is the best state to live in, and Pennsylvania is the worst. Arizona was the 9th lowest in cost of living, whereas Pennsylvania was the 38th highest of 132. Cost of living by city was comparable to states after taking the medians grouped by state. From the summary statistics we obtained an r-squared score of 0.9989 and a p-value of 0.0134 which was an indicator on how well the data could fit the linear model, as well as indicating that it was statistically significant. This lead us to believe that on average as in state tuition rates increased so did out of state tuition rates

Individual Contributions

Maureen:

I helped construct the background and clean data portions of the final project. I also found the coorelation between minimum wage and tuition. I made graphics to support this in the presentation. I helped create the scatterplot for minimum wage by year. I helped write and present the presentation.

Hannah:

I scraped all the data for the project. I cleaned the minimum wage data by removing all non numeric values. I explored the cost of living index data for patterns and graphed it spatially, I also explored the rent index data the same way. I found differing distributions between the two and further explore it with histograms of both and one barplot. I created a minimum wage spatial map and minimum wage scatterplot to explore the relationship between minimum wage and cost of living data. I integrated everyone’s parts into the final report, debugged, and wrote the conclusion. Finally, I collaborated on the presentation.

Omima:

In terms of the project I was able to remove all the missing and null values from the minimum wage dataset. I ran into lots of trouble when I tried to merge different datasets due to different lengths in sizes. This was narrowed down by choosing certain states to represent. After merging I was then able to pick and choose the certain columns pretaining to the questions that needed to be solved. I was then able to make an interactive scatterplot showing the difference in tuition rates by academic year for out of state tuition. Using this I then formulated a prediction model to predict out of state tuition when a given in state tuition value was given. I also helped with the final presentation.

Yuma:

I cleaned the tuition data and cost of living data by removing all non-numeric values. Because the cost of living dataset sometimes has multiple datapoints per state, I struggled to combine datasets and ended up importing them and working with them separately. I found the medians of the costs of living by state in order to simplify the dataset. I created a scatterplot of the minimum wages, and subset the minimum wage data into three groups. I then found the tradeoff between cost of living and minimum wage by best and worst state. I helped create and present the presentation.

References